162 Mr WHEWELL, ON THE NATURE OF THE TRUTH 



Since all bodies, small or large, light or heavy, fall downwards with 

 equal velocities, when we remove or abstract the effect of extraneous 

 circumstances, the motive quantity of the force of gravity on equal 

 bodies is as their masses ; or as their weight, by what has just been said. 



14. For the measure of the motive quantity of force, or of the action 

 and reaction of bodies in motion, we have, therefore, now to chuse 

 among such expressions as MV, and MV^. And our choice must be 

 regulated by finding what is the measure which will enable us to 

 assert, in all cases of action between bodies in motion, that action and 

 reaction are equal and opposite. 



Now the fact is, that either of the above measures may be taken, 

 and each has been taken by a large body of mathematicians. The former 

 however {MV) has obtained the designation which naturally falls to the 

 lot of such a measure ; and is called momentum, or sometimes simply 

 quantity of motion : the latter quantity {MV^) is called vis viva or liv- 

 ing force. 



I have said that either of these measures may be taken : the former 

 must be the measure of action, if we are to measure it by the effect pro- 

 duced in a given time; the latter is the measure if we take the whole 

 effect produced. In either way the third law of motion would be true. 



Thvis if a ball B, lying on a smooth table, be drawn along by a 

 weight A hanging by a thread over the edge of the table, the motion 

 of B is produced by the action of A, and on the other hand the 

 motion of A is diminished by the reaction of B; and the equality 

 of action and reaction here consists in this, that the momentum {MV) 

 which B acquires in any time is equal to that which A loses : that is, 

 so much is taken from the momentum which A would have had, if 

 it had fallen freely in the same time; so that A falls more slowly by 

 just so much. 



But if the weight A fall through a given space from rest, as 1 foot, 

 and then cease to act, the eqviality of action and reaction consists in 

 this, that the vis viva which B acquires on the whole, is equal to the 

 vis viva which A loses ; that is, the vis viva of A thus acting on B is 



